Question: $\vec u = (12,-4)$ $\vec w = (1,-5)$ $\vec w + \vec u= ($
Solution: We add vectors by adding corresponding components: $\begin{aligned} \vec w + \vec u &= (w_x, w_y) + (u_x, u_y) \\\\ &= (w_x+u_x, w_y+u_y) \end{aligned}$ $\begin{aligned} \vec w + \vec u &= (1,-5) + (12,-4) \\\\ &= (1+12,-5+(-4)) \\\\ &= (13,-9) \end{aligned}$ The answer: $ \vec w + \vec u = (13,-9) $